16 weeks pregnant, from week 5 until now i haven't had any meat or anything that has protein. i'm a little concerned if the baby will have any problem?

Concerned: I applaud your concern and strongly suggest that you see the Gynecologist as soon as possible.

Balanced diet needed: You need something from the four basic food groups daily. Yes, you can avoid meat, but alternate protein sources such as beans can be substituted. Pregnancy is the worse time to begin a "fad diet" as you are truly providing nutrients for two and the "victim" of malnourishment is the fetus.